Additional Mathematics 0606: MATRICES (Excluded) Topical Past Paper Questions

Given that $ \mathbf{A} = \begin{pmatrix} 5 & 2 \\ -9 & -3 \end{pmatrix} $ and $ \mathbf{B} = \begin{pmatrix} 2 & 1 \\ 6 & 5 \end{pmatrix} $, find (i) $ \mathbf{A}^{-1} $, [2] (ii) $\mathrm{B}^{2}$, [2] (iii) the matrix C, where $ \mathbf{B}^{-1}C + A = \mathbf{B} $, (iv) the mat…

Given that $ \mathbf{A}=\begin{pmatrix}2 & 3 \\ 1 & 4\end{pmatrix} $ and $ \mathbf{B}=\begin{pmatrix}1 & 4 \\ -2 & 5\end{pmatrix} $, find (i) $ A^{-1} $, (ii) the matrix C such that CA = B, [2] (iii) the matrix D such that $ A^{-1}D + B = I $.

The matrix A is $ \begin{pmatrix}2&1\\4&3\end{pmatrix} $. (i) Find $ (2A)^{-1} $. [3] (ii) Hence solve the simultaneous equations $$ \begin{aligned}&2y+4x+5=0,\\&6y+8x+9=0.\end{aligned} $$